Question 70

A cistern has two taps which fill it in 12 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all the pipes are opened, the empty cistern is full in 20 minutes. How long will the waste pipe take to empty a full cistern?

Solution

Let the capacity of tank be 180 litres.

1st tap fill 180 litres in 15 minutes, 1min= 12 lt fill

2nd tap fill 180 litres in 12 minutes, 1min= 15 lt fill

3rd tap empty 180 litres in x minutes [let]... 1 min empty = 180/x lt

Total filling time = 20 minutes

20*12 + 20*15 - 20*180/x = 180

Solving for x, x = 10 minutes

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